ECE 1100 Introduction to Electrical and Computer Engineering

1
ECE 2317 Applied Electricity and Magnetism
Prof. D. Wilton ECE Dept.
Charge!
Notes 2
Notes prepared by the EM group, University of
Houston.
2
Statics
Definitions Statics frequency f
0 Hz Quasi-statics slow
time variation, f ltlt ? Hz
The electromagnetic field splits into two
independent parts
Electrostatics (q, E) ?Static charge
Magnetostatics (I, B) ?Constant current
w.r.t. time
3
Statics (cont.)
Example
circuit
4
Statics (cont.)
Example f 60 Hz
?0 c / f
c 2.99792458 ? 108 m/s
f 60 Hz
This gives ?0 4.9965?106 m
4,996.5 km
3,097.8 miles
Clearly, most circuits fall into the
static-approximation category at 60 Hz!
5
Statics (cont.)
The following rely on electro(quasi-)static and
magneto(quasi-)static field theory

• circuit theory (e.g, ECE 2300)
• electronics
• power engineering
• magnetics

ECE 2317
Examples of high-frequency systems that are not
modeled by statics

• antennas
• transmission lines
• microwaves
• optics

ECE 3317
6
Charge
electron q e -1.602 x 10-19 C
proton q -e 1.602 x 10-19 C
1 C 1 / 1.602 x10-19 protons
6.242 x 1018 protons
Ben Franklin
7
Charge Density
1) Volume charge density ?v C/m3
?v
?V
uniform cloud of charge density
?Q
8
Charge Density (cont.)
non-uniform (inhomogeneous) volume charge density
non-uniform cloud of charge density
9
Charge Density (cont.)
so
or
10
Charge Density (cont.)
2) Surface charge density ?s C/m2
?s (x,y,z)
?S
non-uniform sheet of charge density
?Q
non-uniform
uniform
11
Charge Density (cont.)
12
Charge Density (cont.)
3) Line charge density ?l C/m
non-uniform line charge density
uniform
non-uniform
13
Charge Density (cont.)
14
Example Find the total charge in the
spherical distribution
z
?v 10 C/m3
a
y
x
Find Q
15
Example Find the total charge in the
non-uniform spherical distribution
z
?v 2r C/m3
a
y
r
x
Find Q
16
Example Find the Equivalent Surface Charge
Density for a Thin Slab of Charge
17
Example Find the Equivalent Line Charge Density
for a Thin Cylinder of Charge
18
Summary of Conversion to Equivalent Charge
Densities
Slab lying in a constant z-plane
Cylinder lying parallel to the z-axis